Question

Jordan 有 $15$ 双运动鞋。其中五分之三是红色，其余是白色。三分之二是高帮，其余是低帮。红色高帮运动鞋占整个收藏的一部分。这个分数的最小可能值是多少？

Jordan owns $15$ pairs of sneakers. Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top. The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction?

$0$

$\dfrac{1}{5}$

$\dfrac{4}{15}$

$\dfrac{1}{3}$

$\dfrac{2}{5}$

答案：C

知识点：容斥原理最优化分数

难度评级：1170

解答：

红色鞋有 $\dfrac{3}{5} \times 15 = 9$ 双，白色鞋有 $6$ 双。另外，高帮鞋有 $\dfrac{2}{3} \times 15 = 10$ 双，低帮鞋有 $5$ 双。为了让红色高帮尽量少，先让全部 $6$ 双白色鞋都是高帮，还需要 $10-6=4$ 双红色高帮，所以最小分数为 $\dfrac{4}{15}$ 。

所以正确答案是 C。

Jordan has $\dfrac{3}{5} \times 15 = 9$ pairs of red sneakers and $6$ pairs of white sneakers. Moreover, $\dfrac{2}{3} \times 15 = 10$ are high-top and $5$ are low-top. If we want to minimize the number of red high-top sneakers, then we can set all $6$ white sneakers to be high-top, leaving $10-6=4$ red sneakers as high-top. Hence, the fraction of red high-top sneakers would be $\dfrac{4}{15}$ .

Thus, C is the correct answer.

2024 AMC 8 第 19 题

答案：C

难度评级：1170

解答：

其他年份的第 19 题